Entanglement of Magnetically Levitated Massive Schr\"odinger Cat States by Induced Dipole Interaction

Quantum entanglement provides a novel way to test short-distance quantum physics in a non-relativistic regime. We provide entanglement-based protocols to potentially test the magnetically induced dipole-dipole interaction and the Casimir-Polder potential between the two nano-crystals kept in a Schrodinger Cat state. Our scheme is based on the Stern-Gerlach (SG) apparatus, where we can witness the entanglement mediated by these interactions for the nano-crystal mass m~10^-19 kg with a spatial superposition size of order 0.1 micron in a trap relying on diamagnetic levitation. We show that it is possible to close the SG interferometer in position and momentum with a modest gradient in the magnetic field.